Subgroups — D₂₈₄₄₉ #72292012

Order 56898.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₉₄₈₃	—	3	1	no	maximal
3	C₃×C₂₉×C₁₀₉	D₃	1	1	yes	characteristic
4	D₃₁₆₁	—	9	1	no	Hall
5	C₂₉×C₁₀₉	D₉	1	1	yes	characteristic, complemented, Hall
6	D₉₈₁	—	29	1	no	maximal, Hall
7	C₉×C₁₀₉	D₂₉	1	1	yes	characteristic, complemented, Hall
8	D₃₂₇	—	87	1	no	—
9	D₂₆₁	—	109	1	no	maximal, Hall
10	C₃×C₁₀₉	D₈₇	1	1	yes	characteristic
11	C₉×C₂₉	D₁₀₉	1	1	yes	characteristic, complemented, Hall
12	D₁₀₉	—	261	1	no	Hall
13	D₈₇	—	327	1	no	—
14	C₁₀₉	D₂₆₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₂₉	D₃₂₇	1	1	yes	characteristic
16	D₂₉	—	981	1	no	Hall
17	C₂₉	D₉₈₁	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	3161	1	no	Hall
19	C₉	D₃₁₆₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	9483	1	no	—
21	C₃	D₉₄₈₃	1	1	yes	characteristic
22	C₂	—	28449	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₉×C₁₀₉	C₂
Frattini	C₃	D₉₄₈₃
socle	C₃×C₂₉×C₁₀₉	D₃
LCS	G ▷ C₉×C₂₉×C₁₀₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.